pH and BUFFERS

pH

The pH = - log [H3O]+ is a measure of the
hydronium concentration of an aqueous solution. The lower the pH the more acidic the
solution. A table summarizing log values for various powers of ten is
shown below.

The Keq of an acid is a measure of the strength of an
acid. For the general acid reaction with water:

HA(aq) + H2O(l) <==> H3O+ + A-, Keq
= ([H3O+][A-])/([HA][H2O])

For a strong acid, Keq > 1 and for a weak acid, Keq < 1.

[H2O] is approximately 55.5 M in a diliute acid
solution, and is essentially constant (since it is present in such great excess). Hence Keq[H2O]
= ([H3O+][A-])/[HA] = Ka.

Ka, the acid constant,is also a constant; for a strong acid, Ka
> 1 and for a weak acid, Ka < 1

Consider the two reactions below in which the concentration of HCl
and CH3COOH are each 0.1 M.:

HCl + H2O ----------> H3O+ + Cl-

At equilibrium, [H3O+] and [Cl- ]
are both approximately 0.1 M and HCl is effectively 0. In actuality, some HCl is left and
can be shown to be 0.000000001 M = 10-9 M.
Hence Ka = ([H3O+][A-])/[HA] = (10-1)(10-1)/10-9
= 107 >> 1.

Just as pH = -log[H3O]+, pKa =
-logKa. In the above examples, the pKa of HCl is -7 while that of
acetic acid is approx. 5.

The pKa of an acid is a measure of the strength of an
acid. It is a constant and does not depend on the concentration of the acid. The lower the
pKa, the more stronger the acid.

Water can act as both a weak acid and a weak base. It can
interact with itself to form the hydronium and hydroxide ion, as shown below:

H2O + H2O ----------> H3O+
+ OH-

In pure water, [H3O+] and [OH-]
are equal (as seen in the equation above) and are each 1x10-7 M. Hence the pH
of neutral water is 7.0

Buffers

Buffer solutions consist of weak acids and salts of weak
acids.They can be created by mixing a solution of a weak acid (such as acetic
acid) with a solution of a salt of a weak acid (such as sodium acetate). Alternatively, buffer solutions can be created by partially
titrating a solution of a weak acid with sodium hydroxide which neutralizes part of the
acid to form the salt of the weak acid, with the sodium ion provided by the added titrant.

Buffer solutions can neutralize the addition of small
amounts of an acid (which reacts with the base product of the weak acid) and
small amounts of a base (which reacts with the weak acid).

Consider what would happen to the pH of pure water (pH = 7) if
either 0.01 mol of NaOH or 0.01 mol of HCl were added to sufficient water to make 1L. The
first solution would now have an [OH-] = 0.01 M and hence a [H3O+]
= 1 x 10-12 M, or a pH = 12. The second solution would have a [H3O+]
= 1 x 10-2 M, or a pH = 2. This examples shows that the addition of a small
amount fo either acid or base to water dramatically changes the pH. Consider the pH of
pure water to be like a balance. Addition of small amounts of either acid or bases
dramatically changes the balance (pH)

pH in the body has to be very tightly controlled. Specifically, the
pH of blood and intracellular spaces can not very much without serious consequences. Two
common buffers systems are

the H2PO4- (weak acid) and HPO42-
(its base)

H2CO3 - carbonic acid (weak acid)
and HCO3-
- bicarbonate (its base)

The later is most important in blood, which is maintained within a
narrow range of 7.35-7.45. This buffer system is a bit more complicated since another
reaction of carbonic acid must be considered - namely the breakdown of carbonic acid to
water and CO2.

CO2(g) + H2O(l) <==> H2CO3(aq)
+ H2O(l) <==> H3O+(aq) + HCO3-(aq)

I demonstrated the reversible formation of carbonic acid in class by
blowing into a water which was made slightly alkaline by the addition of a small amount of
ammonia. The solution become more acidic, as indicated by the change of color of the
solution when phenopthalein was added. The reaction of carbon dioxide with water to form
carbon dioxide can be visualized below:

The two major components of the buffer system of blood are
controlled by two different mechanisms:

H2CO3 is controlled by changing the respiration
rate. If you breath more quickly and deeply (like when you hyperventiallate), you exhale
more CO2. This will decrease the blood carbonic acid by as shown in blue below.
CO2 concentrations decrease,
pulling the equilibria below to the left which decreases H3O+(aq)

CO2(g) + H2O(l) <==>
H2CO3(aq) + H2O(l)
<==> H3O+(aq) + HCO3-(aq)

HCO3-(aq) (bicarbonate) is controlled by the
rate at which it is excreted by the urine.

What happens to the blood pH when the relative amounts ofH2CO3(aq) and HCO3-(aq) change. Lets examine the Ka for the red
part of the equation below, considering carbonic acid as a weak acid.

CO2(g) + H2O(l) <==> H2CO3(aq) + H2O(l)
<==> H3O+(aq) + HCO3-(aq)

Ka = ([H3O+][HCO3-])/[H2CO3]
which can be rearranged to

[H3O+] = Ka[H2CO3]
/[HCO3-]. From this is should be clear that:

if either [H2CO3] increases or [HCO3-]
decreases or both, [H3O+] increases and the pH decreases. If this
decrease in pH is outside of the normal range, the condition is called acidosis.

if either [H2CO3] decreases or [HCO3-]
increases or both, [H3O+] decreases and the pH increases making the
blood more basic or alkaline. If this increase in pH is outside of the normal range, the
condition is called alkalosis.

Two kinds of acidosis are common - respiratory acidosis and
metabolic acidosis.

Metabolic acidosis: This occurs often in burn
patients. Blood plasma leaks into damaged areas which can decrease total blood
volume and flow, decreasing oxygen availability. This will increase anaerobic
metabolism, just as when you are running a fast race and are deprived of oxygen. Lactic
acid builds up in the blood, increasing the H3O+ in the blood,
shifts the equilibrium shown in red below to increase carbonic acid and decrease
bicarbonate:

CO2(g) + H2O(l) <==> H2CO3(aq) + H2O(l)
<==> H3O+(aq) + HCO3-(aq)

This decreased pH causes the injured person to break harder to get
rid of CO2, which by Le Chateliers principle causes a helpful decrease in
carbonic acid as shown in blue below:

CO2(g) + H2O(l) <==>
H2CO3(aq) + H2O(l)
<==> H3O+(aq) + HCO3-(aq)

If the damage is to great so the person can't breath well, shock can
develop.

Respiratory acidosis: This occurs in burn victims who have
inhaled much smoke and can't breath well. Likewise it occurs in pulmonary diseases such as
emphysema or a physical obstruction which hinders respiration. This causes CO2
to build up, increasing carbonic acid and decreasing blood pH as shown below in red: